Computer program for generating 1-bit image data from multiple-bit image data

ABSTRACT

A computer program for and a method of generating 1-bit image data from multiple-bit image data, by a process which comprises the steps of: receiving multiple-bit image data comprising multiple-bit pixel values; and deriving from the multiple-bit pixel values 1-bit image data comprising “on” and “off” pixel values, each pixel value of the 1-bit image data corresponding to a pixel of an output medium, which pixel an output device would attempt to mark when printing the 1-bit image data if the pixel value were “on”, the 1-bit image data producing when printed an image constituted by a plurality of densities of dot, the dots are arranged such that, at least for densities of dots greater than a first threshold density, at least a majority of dots form a pair with at least one horizontally or vertically adjacent dot, and for densities of dots less than a second threshold density, the image is substantially free of blocks of 2*2 horizontally and vertically adjacent dots, the second threshold density being greater than the first threshold density, additionally or alternatively, the dots being arranged such that, for densities of dots greater than a first threshold density and less than a second threshold density, at least a majority of dots form a pair with one horizontally or vertically adjacent dot, for densities of dots greater than the second threshold density and less than a third threshold density, at least a majority of pairs of horizontally and vertically adjacent dots form a triplet with one horizontally or vertically adjacent dot, and for densities of dots greater than the third threshold density and less than a fourth threshold density, at least a majority of dots form triplets with two horizontally or vertically adjacent dots, the second threshold density being greater than the first threshold density, the third threshold density being greater than the second threshold density, and the fourth threshold density being greater than the third threshold density, additionally or alternatively the dots are arranged such that, for densities of dots greater than a first threshold density, at least a majority of dots form a pair with a horizontally or vertically adjacent dot, for densities of dots greater than a second threshold density, some pairs of dots form a triplet with a horizontally or vertically adjacent dot, and for densities of dots greater than a third threshold density, at least a majority of pairs of dots form a triplet with a horizontally or vertically adjacent dot, the second threshold density being greater than the first threshold density and the third threshold density being greater than the second threshold density, and for each density of dots between the first and third threshold densities, numbers of dots constituting substantially all isolated groups of horizontally and vertically adjacent dots differing by no more than one.

FIELD OF THE INVENTION

This invention relates to a computer program for generating 1-bit imagedata from multiple-bit image data, and more particularly to a computerprogram for generating 1-bit image data that, when printed, produce animage constituted by a plurality of densities of dots and having littleor no appearance of graininess or patterning to a human eye.

BACKGROUND TO THE INVENTION

Computer programs for generating 1-bit image data comprising “on” and“off” pixel values from multiple-bit image data, which 1-bit image data,when printed, produce an image that is constituted by dots, are wellknown, the process of generating the 1-bit image data being known as“screening”.

Such computer programs fall into two broad categories. The firstcategory carry out so-called “amplitude modulated” (AM) screening togenerate 1-bit image data that, when printed, produce an image that isconstituted by a plurality of sizes of dots, the dots being regularlyspaced throughout the image.

The second category carry out so-called “frequency modulated” (FM)screening to generate 1-bit image data that, when printed, produce animage that is constituted by a plurality of densities of dots, the dotstypically all having the same size.

There are various problems with AM screening, the most significant ofwhich are colour shift and formation of Moire patterns when two or morescreened images are overlaid, as occurs in colour printing.

These problems are caused by the regular spacing of the dots and do notarise in FM screening. There are, however, different problems with FMscreening, the most significant of which are the appearance ofgraininess of the image and the appearance of patterning of the image.

The appearance of graininess occurs because of the irregular spacing ofthe dots throughout the image. Whereas the human eye readily disregardsthe regularly spaced individual dots making up an image produced by AMscreening, it struggles to disregard the irregularly spaced individualdots making up an image produced by FM screening, which gives the imagethe appearance of graininess. This is exacerbated where the imagecontains clusters of adjacent dots among irregularly spaced individualdots, as such clusters are extremely conspicuous.

Each pixel value of the 1-bit image data corresponds to a pixel of anoutput medium. When printing the 1-bit image data, an output deviceattempts to mark those pixels of the output medium which correspond to“on” pixel values of the 1-bit image data. Although a few output devicescan fully mark a pixel of the output medium without marking adjacentpixels, most output devices either do not fully mark the pixel, whichgives rise to so-called “dot loss”, or also mark adjacent pixels, whichgives rise to so-called “dot gain”.

The appearance of patterning results from dot gain because pairs ofdiagonally adjacent marked pixels exhibit more dot gain than pairs ofhorizontally or vertically adjacent marked pixels. Dot gain also causesisolated pixels corresponding to “off” pixel values of the 1-bit imagedata, referred to in this specification as “non-pixels”, i.e. non-pixelssurrounded by marked pixels, to have a greater proportion of their areasmarked, if not all of their areas, as a result of marking thesurrounding pixels, than the non-pixels of isolated pairs ofhorizontally or vertically adjacent non-pixels.

FIG. 1 represents a portion 10 of an output medium on which a pair ofhorizontally adjacent pixels 12 and 14, a pair of vertically adjacentpixels 16 and 18, and a pair of diagonally adjacent pixels 20 and 22have been marked by an output device that produces dot gain. As can beseen from FIG. 1, marking of the pair of horizontally adjacent pixels 12and 14 causes six regions 24, 26, 28, 30, 32 and 34 of the surroundingpixels also to be marked as a result of dot gain. Marking of the pair ofvertically adjacent pixels 16 and 18 also causes six regions 36, 38, 40,42, 44 and 46 also to be marked. Marking of the pair of diagonallyadjacent pixels 20 and 22, however, causes eight regions 48, 50, 52, 54,56, 58, 60 and 62 also to be marked. The pair of diagonally adjacentmarked pixels 20 and 22 would therefore appear darker than the pairs ofhorizontally and vertically adjacent marked pixels 12 and 14 and 16 and18.

Portions of an image containing isolated pairs of diagonally adjacentmarked pixels, such as marked pixels 20 and 22 of FIG. 1, or multiplelines of diagonally adjacent marked pixels, can have an appearance ofpatterning, because the isolated pairs of diagonally adjacent markedpixels and the multiple lines of diagonally adjacent marked pixelsappear darker than nearby pairs of horizontally and vertically adjacentmarked pixels. Portions of an image containing both isolated non-pixelsand isolated pairs of horizontally and vertically adjacent non-pixelscan also have an appearance of patterning, because the isolated pairs ofhorizontally and vertically adjacent non-pixels appear much lighter thanthe isolated non-pixels.

For these reasons of graininess and patterning, although FM screeninghas the potential to produce better printed images than AM screening, ithas not been as widely accepted as AM screening.

SUMMARY OF THE INVENTION

According to the invention there is provided a computer program forexecuting on a computer system a computer process for generating 1-bitimage data from multiple-bit image data, the process comprising thesteps of:

receiving multiple-bit image data comprising multiple-bit pixel values;and

deriving from the multiple-bit pixel values 1-bit image data comprising“on” and “off” pixel values, each pixel value of the 1-bit image datacorresponding to a pixel of an output medium, which pixel an outputdevice would attempt to mark when printing the 1-bit image data if thepixel value were “on”, the 1-bit image data producing when printed animage constituted by a plurality of densities of dots, the dots beingarranged such that, at least for densities of dots greater than a firstthreshold density, at least a majority of dots form a pair with at leastone horizontally or vertically adjacent dot, and for densities of dotsless than a second threshold density, the image is substantially free ofblocks of 2*2 horizontally and vertically adjacent dots, the secondthreshold density being greater than the first threshold density.

The invention can provide a computer program that, in certainembodiments, can generate 1-bit image data that, when printed, producean image that has relatively little appearance of graininess in portionsof the image of which the densities of dots are relatively low, be 2*2blocks of horizontally and vertically adjacent dots would be conspicuousare substantially free of such blocks of dots.

In this specification, “substantially free of” means present insufficiently low numbers as to be not readily discernible by the humaneye.

The multiple-bit image data may, for example, comprise 8-bit continuoustone raster image data.

Some output devices mark pixels of an output medium corresponding topixel values of the 1-bit image data that are one, whereas other outputdevices mark pixels corresponding to pixel values of the 1-bit imagedata that are zero. For the avoidance of doubt, “on” pixel values of the1-bit image data can be either one or zero, the “off” pixel values thenbeing zero or one, respectively.

The step of deriving the 1-bit image data may advantageously compriseusing a threshold array.

In a preferred embodiment of the invention, the step of deriving the1-bit image data comprises using an error diffusion algorithm.

For the purposes of this specification, an “output medium” is a mediumthat can be marked so as to cause an image to appear on the medium andan “output device” is a device operable to mark an output medium.Examples of output media include paper, printing plates for use inprinting presses and photosensitive film for use in making printingplates. Examples of output devices include inkjet printers,computer-to-film imagesetters, computer-to-plate systems and printingpresses.

The dots may advantageously also be arranged such that, at least fordensities of dots greater than the first threshold density and less thana third threshold density, at least a majority of dots form a pair withone horizontally or vertically adjacent dot, the third threshold densitybeing less than the second threshold density.

The dots may advantageously also be arranged such that, for alldensities of dots, at least a majority of dots form a pair with at leastone horizontally or vertically adjacent dot.

It may be, however, that in portions of the image of which the densitiesof dots are very low, pairs of dots are conspicuous.

Alternatively, therefore, the dots may advantageously also be arrangedsuch that, for densities of dots less than the first threshold density,at least some of the dots have no adjacent dots.

The dots may advantageously also be arranged such that, for densities ofdots greater than a fourth threshold density, at least one dot of atleast a majority of pairs of dots forms pairs with two horizontally orvertically adjacent dots, the fourth threshold density being greaterthan the third threshold density and less than the second thresholddensity.

The dots may advantageously also be arranged such that, for densities ofdots less than a fifth threshold density, at least a majority of dotsform chains of horizontally or vertically adjacent dots, the chainshaving similar numbers of dots, and the fifth threshold density beingless than the second threshold density.

Where the dots are so arranged, the invention can provide a computerprogram that can generate 1-bit image data that, when printed, producean image that has little or no appearance of graininess in portions ofthe image of which the densities of dots are relatively low, becauseportions of the image of which the densities of the dots aresufficiently low that chains of horizontally or vertically adjacent dotshaving substantially different numbers of dots, or 2*2 blocks ofhorizontally and vertically adjacent dots, would be conspicuous, aresubstantially free of such chains or blocks of dots.

A portion of an image that could be occupied by a dot, but is not sooccupied, will be referred to in this specification as a “non-dot”.

It will be apparent that the problems of conspicuous chains ofhorizontally or vertically adjacent dots having different numbers ofdots, and conspicuous blocks of 2*2 horizontally and vertically adjacentdots, in portions of images of which the densities of dots are low,which problems are solved by this invention, have analogues inconspicuous chains of horizontally or vertically adjacent non-dotshaving substantially different numbers of dots, and conspicuous blocksof 2*2 horizontally and vertically adjacent non-dots, in portions ofimages of which the densities of dots are high.

In portions of images of which the densities of dots are high, chains ofhorizontally or vertically adjacent non-dots having different numbers ofnon-dots, and blocks of 2*2 horizontally and vertically adjacentnon-dots, when surrounded by dots, can be conspicuous and give anappearance of graininess, in the same way as such chains and blocks ofdots can give an appearance of graininess.

Thus the dots may advantageously also be arranged such that, at leastfor densities of dots less than a sixth threshold density, at least amajority of portions of the image that could be occupied by a dot, butare not so occupied, form a pair with at least one horizontally orvertically adjacent non-dot, and for densities of dots greater than aseventh threshold density, the image is substantially free of blocks of2*2 horizontally and vertically adjacent non-dots, the sixth thresholddensity being greater than the seventh threshold density.

The dots may advantageously also be arranged such that, at least fordensities of dots less than the sixth threshold density and greater thanan eighth threshold density, at least a majority of non-dots form a pairwith one horizontally or vertically adjacent non-dot, the eighththreshold density being greater than the seventh threshold density.

The dots may advantageously also be arranged such that, for alldensities of dots, at least a majority of non-dots form a pair with atleast one horizontally or vertically adjacent non-dot.

It may be, however, that in portions of the image of which the densitiesof dots are very high, pairs of non-dots are conspicuous.

Alternatively, therefore, the dots may advantageously also be arrangedsuch that, for densities of dots greater than the sixth thresholddensity, at least some of the non-dots have no adjacent non-dots.

Where the 1-bit image data are to be printed using an output device thatproduces relatively little dot gain, the arrangement of the dots suchthat at least some of the non-dots have no adjacent non-dots can beused, because dot gain of the dots surrounding the non-dots will notsignificantly reduce the size of the non-dots.

Where the 1-bit image data are to be printed using an output device thatproduces significant dot gain, however, the arrangement of the dots suchthat at least some of the non-dots have no adjacent non-dots cannot beused, because dot gain of the dots surrounding the non-dots willsignificantly reduce the size of the non-dots, or even cause them todisappear.

The dots may advantageously also be arranged such that, for densities ofdots less than a ninth threshold density, at least one non-dot of atleast a majority of pairs of non-dots forms pairs with two horizontallyor vertically adjacent non-dots, the ninth threshold density being lessthan the eighth threshold density and greater than the seventh thresholddensity.

The dots may advantageously also be arranged such that, for densities ofdots greater than a tenth threshold density, at least a majority ofnon-dots form chains of horizontally or vertically adjacent non-dots,the chains having similar numbers of non-dots, and the tenth thresholddensity being greater than the seventh threshold density.

Where the dots are so arranged, the invention can provide a computerprogram that can generate 1-bit image data that, when printed, producean image that has little or no appearance of graininess in portions ofthe image of which the densities of dots are relatively high, becauseportions of the image of which the densities of the dots aresufficiently high that chains of horizontally or vertically adjacentnon-dots having substantially different numbers of non-dots, or 2*2blocks of horizontally or vertically adjacent non-dots, would beconspicuous, are substantially free of such chains or blocks ofnon-dots.

In the preferred embodiment of the invention the second thresholddensity, for densities of dots less than which the image issubstantially free of blocks of 2*2 horizontally and vertically adjacentdots, is halfway between a minimum available density of dots and amaximum available density of dots. That is to say, in portions of theimage of the second threshold density the number of dots is equal to thenumber of non-dots.

In the preferred embodiment of the invention the seventh thresholddensity, for densities of dots greater than which the image issubstantially free of blocks of 2*2 horizontally and vertically adjacentnon-dots, is also halfway between a minimum available density of dotsand a maximum available density of dots.

This is desirable from the point of view of simplicity of the computerprogram, because the same rules that determine the placement of dots inthe image can be used to determine the placement of non-dots in theimage.

Each dot of the image may advantageously correspond to a single pixelvalue of the 1-bit image data. In this way each pixel of an outputmedium that is marked by an output device constitutes a dot of theimage.

Many output devices cannot reliably mark an isolated pixel or anisolated small group of pixels of an output medium, so that some of thepixels of the output medium that correspond to “on” pixel values of the1-bit image data would not reliably be marked by such output devices.

to Thus each dot of the image may advantageously correspond to aplurality of pixel values of the 1-bit image data. In this way each dotof the image is constituted by two or more pixels of an output mediumthat are marked by an output device.

The plurality of pixel values may advantageously correspond to a row oftwo or more horizontally adjacent pixels of an output medium or a columnof two or more vertically adjacent pixels of an output medium.

The plurality of pixel values preferably correspond to a rectangular orsubstantially rectangular block of horizontally and vertically adjacentpixels of an output medium.

It will be apparent, however, that the plurality of pixel values couldcorrespond to any pixels of an output medium, the pixels forming anyrepeating shape or pattern.

Where each dot of the image corresponds to a plurality of pixel values,each of the plurality of pixel values may advantageously be “on”.

This can produce dots that can be reliably reproduced on an outputmedium by an output device that cannot reliably mark an isolated pixelof the output medium.

Alternatively, at least one of the plurality of pixel values mayadvantageously be “off”.

Where each dot of the image corresponds to a plurality of pixel values,which correspond to a rectangular or substantially rectangular block ofhorizontally and vertically adjacent pixels of an output medium and atleast one of the plurality of pixel values is “off”, for densities ofdots less than the first threshold density, for at least a majority ofpairs of horizontally adjacent dots, at least the pixel valuescorresponding to a first column of vertically adjacent pixels and a lastcolumn of vertically adjacent pixels of the pair of blocks ofhorizontally and vertically adjacent pixels may advantageously be “off”,and for at least a majority of pairs of vertically adjacent dots, atleast the pixel values corresponding to a first row of horizontallyadjacent pixels and a last row of horizontally adjacent pixels of thepair of blocks of horizontally and vertically adjacent pixels mayadvantageously be “off”.

In this way, the size of pairs of dots can be reduced in portions of theimage of which the densities of dots are sufficiently low thatfull-sized pairs of dots would be conspicuous.

Where each dot of the image corresponds to a plurality of pixel values,which correspond to a row of horizontally adjacent pixels or a column ofvertically adjacent pixels, for at least a majority of the dots a pixelvalue corresponding to a first or last pixel of the row, or to a firstor last pixel of the column, may advantageously be “off”.

Where each dot of the image corresponds to a plurality of pixel values,which correspond to a rectangular or substantially rectangular block ofhorizontally and vertically adjacent pixels of an output medium and atleast one of the plurality of pixel values is “off”, alternatively oradditionally, for at least a majority of dots, at least some of thepixel values corresponding to at least one of first and last columns ofvertically adjacent pixels and at least one of first and last rows ofhorizontally adjacent pixels of the block of horizontally and verticallyadjacent pixels may advantageously be “off”.

In this way, dots can be obtained such that horizontally adjacent andvertically adjacent dots exhibit the same amount of dot gain as pairs ofdiagonally adjacent dots, so that an image can be produced that issubstantially free of the appearance of patterning. It is to be noted,however, that pairs of diagonally adjacent dots only occur as part oftwo pairs of dots.

Moreover, such dots are reduced in size, which has the additionaladvantage that isolated dots, i.e. dots with no adjacent dots, whichmight appear conspicuous if full-sized dots were used, are lessconspicuous.

The step of deriving from the multiple-bit pixel values 1-bit image datacomprising “on” and “off” pixel values may advantageously furthercomprise identifying multiple-bit pixel values of the multiple-bit imagedata equal to a minimum available multiple-bit pixel value or a maximumavailable multiple-bit pixel value, and for each minimum availablemultiple-bit pixel value generating a corresponding “off” pixel value ofthe 1-bit image data, and for each maximum available multiple-bit pixelvalue generating a corresponding “on” pixel value of the 1-bit imagedata.

Where the step of deriving the 1-bit image data includes this operation,the invention can provide a computer program that can generate 1-bitimage data that, when printed, produce an image in which fine details,such as text and straight edges in graphics, which details are presentin an image represented by the multiple-bit image data, are preserved.

The invention also lies in an output device in which a program accordingto the invention is stored.

The invention can also be seen to lie in a computer program for, ormethod of, generating one-bit image data from multiple bit image data,by a process comprising steps of receiving multiple bit image datacomprising multiple bit pixel values; deriving from the multiple bitpixel values one bit image data comprising “on” and “off” pixel values,each pixel value of the one-bit image data corresponding to a pixel ofan output medium, which pixel output device would attempt to mark whenprinting the one-bit image data if the pixel value were “on”, theone-bit image data producing, when printed, an image constituted by aplurality of dots arranged with a plurality of number densities;determining whether each said density is above a first threshold andbelow a second, higher threshold; and ensuring that the dots arearranged with the relationship between each dot and its adjacent dot ordots satisfying at least one criterion which is dependent on saiddetermination, thereby to reduce or avoid the appearance of graininessor patterning in the printed image.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will now be described, by way of example, with referenceto the accompanying drawings, in which:

FIG. 1 is a schematic representation of a portion of an output medium;

FIG. 2 is a flow diagram of a computer process executed by a computerprogram in accordance with the invention;

FIG. 3 is a schematic representation of a portion of an array of 8-bitpixel values that constitute multiple-bit image data;

FIG. 4 is a flow diagram of part of the computer process of FIG. 2;

FIGS. 5 and 6 are schematic representations of portions of an outputmedium;

FIG. 7 is a schematic representation of a portion of an array of 1-bitpixel values that constitute a second intermediate array used togenerate 1-bit image data;

FIGS. 8 a, 8 b and 8 c are typical patterns of dots from an imageproduced by the computer program of the invention;

FIG. 9 is a typical pattern of dots from an image produced by a knowncomputer program; and

FIG. 10 is a schematic representation of a portion of an output medium.

DETAILED DESCRIPTION OF AN EMBODIMENT

FIG. 2 shows a computer process 100 that is executed by a computerprogram in accordance with the invention. The computer process comprisesfirst and second steps 110 and 120 respectively.

The first step 110 comprises receiving multiple-bit image data in theform of 8-bit continuous tone raster image data. FIG. 3 representsspecimen image data 200, which are part of an array of X*Y pixel valuesin the range 0 to 255.

The second step 120 is shown in FIG. 4 and comprises the operations ofreceiving 130 values defining the size of dot that is to be used toproduce an image using the computer program, receiving 140 instructionsas to whether pairs of dots are to be used in portions of the image ofwhich the densities of dots are low, if so, receiving 150 instructionsas to whether the pairs of dots to be used in portions of the image ofwhich the densities of dots are low are to be of a reduced size,receiving 160 instructions as to whether all dots are to be of a reducedsize, and deriving 170 1-bit image data in the form of an array of X*Y“on” and “off” pixel values from the multiple-bit image data, which,when printed on an output medium by an output device, produce an imageconstituted by dots of the specified size or sizes.

The operation 130 of receiving values defining the size of dot that isto be used to produce the image comprises receiving a first value M thatdefines a width in pixels of the dot, and a second value N that definesa height in pixels of the dot. Typically M and N are selected to beequal, so that the dot is square, although this is not essential. Thecomputer program provides for the use of dots from 1*1 pixel up to 6*6pixels.

It will be appreciated that it is desirable for the dots that constitutethe image to be as small as possible, because if individual dots of theimage cannot be discerned by the human eye, the image is less likely tohave an appearance of graininess.

However, although some output devices such as inkjet printers arecapable of reliably marking an isolated pixel of an output medium, thatis a pixel surrounded by unmarked pixels, many output devices such asprinting presses are incapable of marking an isolated pixel, so thatthese devices could not reliably print an image constituted by 1*1 pixeldots. Indeed, many such devices cannot reliably mark 2*2 pixel dots,although most can reliably mark 3*3 or 4*4 pixel dots. Typically thesmallest dot that can reliably be marked by the output device with whichthe image is to be printed would be selected.

In an image constituted by 3*3 or 4*4 pixel dots, isolated pairs ofadjacent dots, that is to say pairs of adjacent dots surrounded bynon-dots, may be conspicuous. This will certainly be the case where 5*5or 6*6 pixel dots are used. It may therefore be desirable to useisolated dots instead of isolated pairs of adjacent dots. Whetherisolated dots or isolated pairs of adjacent dots are used in portions ofthe image of which the densities of dots are low is determined by theinstructions received in operation 140.

If in operation 140 it is determined that isolated pairs of adjacentdots are to be used, and not isolated dots, the size of the isolatedpairs of dots can be reduced in operation 150. The reduced-size isolatedpairs of adjacent dots are less conspicuous than full-sized pairs ofadjacent dots, but more conspicuous than isolated dots.

FIG. 5 represents a portion 300 of an output medium on which afull-sized pair 310 of horizontally adjacent 4*4 pixel dots 312 and 314,a full-sized pair 316 of vertically adjacent 4*4 pixel dots 318 and 320,a reduced-sized pair 322 of horizontally adjacent 4*4 pixel dots 324 and326, and a reduced-sized pair 328 of vertically adjacent 4*4 pixel dots330 and 332 have been marked. In order to mark the full-sized pairs ofdots 310 and 316, rectangular blocks of 8*4 pixels and 4*8 pixels,respectively, i.e. blocks of 32 horizontally and vertically adjacentpixels, are marked. In order to mark the reduced-sized pairs of dots 322and 328, rectangular blocks of 6*4 pixels and 4*6 pixels, respectively,i.e. blocks of 24 horizontally and vertically adjacent pixels, aremarked. By comparing the full-sized pair 310 of horizontally adjacentdots with the reduced-sized pair 322 of horizontally adjacent dots, itcan be seen that the reduced-sized pair 322 is obtained by not markingfirst and last columns of vertically adjacent pixels that would bemarked in order to obtain the full-sized pair 310. It can also be seenthat the reduced-sized pair 328 of vertically adjacent dots is obtainedby not marking first and last rows of horizontally adjacent pixels thatwould be marked in order to obtain the full-sized pair 316. It is to benoted that a single full-sized dot is obtained by marking a rectangularblock of 4*4 pixels, i.e. 16 pixels. Thus a reduced-sized pair ofadjacent dots constituted by 24 marked pixels can be seen to be halfwayin size between a full-sized single dot constituted by 16 marked pixelsand a full-sized pair of dots constituted by 32 marked pixels.

Where the image is to be printed using an output device that producesdot gain, it may be desirable to use reduced-sized dots for all of thedots that constitute the image. Whether full-sized dots or reduced-sizeddots are used is determined by the instructions received in operation160.

FIG. 6 represents a portion 400 of an output medium on which a pair 410of reduced-sized vertically adjacent 4*4 pixel dots 412 and 414, a pair416 of reduced-sized horizontally adjacent 4*4 pixel dots 418 and 420, apair 422 of reduced-sized diagonally adjacent 4*4 pixel dots 424 and426, and a full-sized 4*4 pixel dot 428 have been marked by an outputdevice that produces dot gain. From FIG. 6 it can be seen that thereduced-sized dots 412, 414, 418, 420, 424 and 426 are obtained by notmarking a first row of horizontally adjacent pixels and a first columnof vertically adjacent pixels that would be marked in order to obtainthe full-sized dot 428.

If the output device produces sufficient dot gain, there may be no gapvisible between the last row of horizontally adjacent marked pixels ofthe dot 412, for example, and the first row of horizontally adjacentmarked pixels of the dot 414. If the dot gain is insufficient to closethe gap, it is envisaged that one or more of the three unmarked pixels430, 432 and 434 between the dots 412 and 414 may be marked.

From FIG. 6 it can be seen that marking of each of the dots 412, 414,418, 420, 424 and 426 causes twelve regions of the surrounding pixelsalso to be marked as a result of dot gain, regardless of whether the dotis horizontally, vertically or diagonally adjacent to another dot. Theregions marked as a result of marking the pixels of the dot 424 aredenoted by reference numerals 436, 438, 440, 442, 444, 446, 448, 450,452, 454, 456 and 458. The effect of this is that pairs of diagonallyadjacent dots appear no darker than pairs of horizontally or verticallyadjacent dots, thus avoiding the appearance of patterning that haspreviously affected images produced using FM screening.

The operation 170 of deriving the 1-bit image data from the multiple-bitimage data will now be described in detail, assuming initially that inoperation 130 a 4*4 pixel dot was specified, in operation 140instructions to use pairs of dots in portions of the image of which thedensities of dots are low were received, in operation 150 instructionsnot to use reduced-sized isolated pairs of dots were received, and inoperation 160 instructions not to use reduced-sized dots were received.

The array of X*Y 8-bit pixel values is divided into (X/4)*(Y/4)sub-arrays of 4*4 8-bit pixel values. Nine such sub-arrays are shown inFIG. 3, denoted by reference numerals 210, 212, 214, 216, 218, 220, 222,224 and 226. The average of the pixel values of each such sub-array iscalculated and a first intermediate array of (X/4)*(Y/4) average pixelvalues is generated. A second intermediate array of (X/4)*(Y/4) 1-bitpixel values is also generated, each pixel value of the secondintermediate array corresponding to an average pixel value of the firstintermediate array, and being set to “off” by default.

It should be noted that where a 1*1 pixel dot is specified, the firstand second intermediate arrays are not generated, but the 1-bit imagedata is instead derived directly from the 8-bit image data, without theuse of the intermediate arrays.

The first intermediate array is processed using a highly modified errordiffusion algorithm, which is applied to each average pixel value of thefirst intermediate array in turn, starting at the top left average pixelvalue, working along the first row of average pixel values to the topright average pixel value, proceeding to the rightmost average pixelvalue of the second row of average pixel values, working along thesecond row of average pixel values to the leftmost average pixel valueof the second row of average pixel values, proceeding to the leftmostaverage pixel value of the third row, working along the third row ofaverage pixel values to the rightmost average pixel value, and so on.

For each average pixel value in turn, unless the corresponding pixelvalue of the second intermediate array has already been set to “on”, theerror diffusion algorithm determines from the average pixel value andany diffused error whether the corresponding pixel value of the secondintermediate array should be set to “on”. If it is determined that thecorresponding pixel value should be set to “on”, a first series of testsare applied based on the average pixel value. If the results of thetests are all negative, the corresponding pixel value is set to “on”,otherwise the corresponding pixel value remains set to “off”. Similarly,if it is determined by the error diffusion algorithm that thecorresponding pixel value should be set to “off”, a second series oftests are applied based on the average pixel value. If the results ofthe tests are all negative, the corresponding pixel value remains set to“off”. If any of the results of the tests is positive, the correspondingpixel value is set to “on”.

FIG. 7 represents a portion 500 of the second intermediate array, “on”pixel values being represented by shaded squares and “off” pixel valuesbeing represented by unshaded squares. The square 510 represents thepixel value that corresponds to the average pixel value calculated fromthe sub-array 210 of FIG. 3. The squares 512, 514, 516, 518, 520, 522,524 and 526 correspond to the average pixel values calculated from thesub-arrays 212, 214, 216, 218, 220, 222, 224 and 226 of FIG. 3.

The average pixel value calculated from the sub-array 210 of FIG. 3 is134 to the nearest whole number. As the average pixel value is greaterthan 127, the error diffusion algorithm determines that thecorresponding pixel value of the second intermediate array should be setto “on”.

The following series of tests are therefore carried out.

-   -   (a) If the average pixel value is less than or equal to 50%,        i.e. 127 for 8-bit image data, would setting the pixel value of        the second intermediate array to “on” cause a row of more than 4        horizontally adjacent “on” values or a column of more than 4        vertically adjacent “on” values?    -   (b) If the average pixel value is greater than 50% and less than        or equal to 62.5%, would setting the pixel value of the second        intermediate array to “on” cause a row of more than int        (4+((average pixel value−50)/12.5)*7) horizontally adjacent “on”        values or a column of more than int (4+((average pixel        value−50)/12.5)*7) vertically adjacent “on” values?    -   (c) If the average pixel value is less than or equal to 28.125%,        would setting the pixel value of the second intermediate array        to “on” cause a chain of 3 horizontally and/or vertically        adjacent “on” values?    -   (d) If the average pixel value is less than or equal to 50%,        would setting the pixel value to “on” cause a block of 2*2        horizontally and vertically adjacent “on” values?    -   (e) If the average pixel value is greater than 50% and less than        56.25%, would setting the pixel value to “on” cause a block of        2*3 or 3*2 horizontally and vertically adjacent “on” values?    -   (f) If the average pixel value is greater than 56.25% and less        than or equal to 62.5%, would setting the pixel value to “on”        cause a block of 3*3 or 2*4 or 4*2 horizontally and vertically        adjacent “on” values?    -   (g) If the average pixel value is greater than 62.5% and less        than or equal to 68.75%, would setting the pixel value to “on”        cause a block of 3*4 or 4*3 or 2*6 or 6*2 horizontally and        vertically adjacent “on” values?    -   (h) If the average pixel value is greater than 68.75% and less        than or equal to 75%, would setting the pixel value to “on”        cause a block of 4*4 or 3*5 or 5*3 or 2*7 or 7*2 horizontally        and vertically adjacent “on” values?    -   (i) If the average pixel value is greater than 75% and less than        or equal to 82.5%, would setting the pixel value to “on” cause a        block of 4*5 or 5*4 or 3*7 or 7*3 or 2*10 or 10*2 horizontally        and vertically adjacent “on” values?

In this instance, because the average pixel value is the first pixelvalue of the first intermediate array to be processed, all of the pixelvalues of the second intermediate array are “off” by default and theresults of all of the tests are negative. The pixel value 510 istherefore set to “on”.

Had the error diffusion algorithm determined that the correspondingpixel value should remain “off”, a corresponding series of tests wouldhave been carried out. The test corresponding to test (a), for example,is “If the average pixel value is greater than or equal to 50%, wouldsetting the pixel value of the second intermediate array to “off” causea row of more than 4 horizontally adjacent “off” values or a column ofmore than 4 vertically adjacent “off” values?”. The test correspondingto test (i) is “If the average pixel value is less than 25% and greaterthan or equal to 17.5%, would setting the pixel value to “off” cause ablock of 4*5 or 5*4 or 3*7 or 7*3 or 2*10 or 10*2 horizontally andvertically adjacent “off” values?”.

By setting the pixel value of the second intermediate array to “on”, thecorresponding average pixel value of 134 of the first intermediate arrayhas effectively been represented by a pixel value of 255, the pixelvalues of the second array being constrained to be either 0 or 255,which correspond to “off” and “on” respectively. An error value of255−134=121 is therefore generated and subtracted from the average pixelvalue of the sub-array 212.

With the exception of portions of the image of which the densities ofdots are low, and only then if it was determined in operation 140 thatsingle dots are to be used in portions of the image of which thedensities of dots are low, a dot must always form a pair with ahorizontally or vertically adjacent dot. This means that a horizontallyor vertically adjacent pixel value of the second intermediate array mustalso be set to “on”, so that the image contains a pair of horizontallyor vertically adjacent dots. The horizontally or vertically adjacentpixel value is chosen at random. In this instance, the verticallyadjacent pixel value 520 is chosen and set to “on”.

Processing of the first intermediate array moves to the average pixelvalue calculated from the sub-array 212. The average pixel value is 141to the nearest whole number. The result of subtracting the error of 121diffused from the previous average pixel value from the average pixelvalue 141 is 20. As this is less than 127, the error diffusion algorithmdetermines that the pixel value 512 of the second intermediate arrayshould remain “off”.

The results of the corresponding series of tests are all negative so thepixel value 512 remains “off”. Again, with the exception of portions ofthe image of which the densities of dots are high, and only then if itwas determined in operation 140 that single dots are to be used inportions of the image of which the densities of dots are low, and thatalso therefore single non-dots are to be used in portions of the imageof which the densities of dots are high, a non-dot must always form apair with a horizontally or vertically adjacent non-dot. This means thata pixel value horizontally or vertically adjacent to the pixel value 512must also remain “off”. In this instance the horizontally adjacent pixelvalue 514 is chosen.

By maintaining the pixel value 512 “off”, the result of thecorresponding average pixel value less the error diffused from theprevious pixel value, that is 20, has effectively been represented by apixel value of 0. An error value of 0−20=−20 is therefore generated andsubtracted from the average pixel value of the sub-array 214.

Processing of the first intermediate array moves to the average pixelvalue calculated from the sub-array 214. The average pixel value is 137to the nearest whole number. The result of subtracting the error of −20diffused from the previous average pixel value from the average pixelvalue 137 is 157. Although this is greater than 127, the pixel value 514has already been determined to remain “off”, so as to form a pair withthe “off” pixel value 512. An error value of 0-157=−157 is thereforegenerated and subtracted from the average pixel value of the sub-array516.

Processing moves to the average pixel value calculated from thesub-array 216. The average pixel value is 139 to the nearest wholenumber. The result of subtracting the error of −157 diffused from theprevious average pixel value from the average pixel value 139 is 296. Asthis is greater than 127, the error diffusion algorithm determines thatthe pixel value 516 of the second intermediate array should be set to“on”.

The results of the series of tests are all negative so the pixel value516 is set to “on”. The horizontally adjacent pixel value 518 is chosenas the adjacent pixel that is to be set to “on” so that the pixel values516 and 518 form a pair. An error value of 255−296=−41 is generated andsubtracted from the average pixel value of the sub-array 218.

Processing moves to the average pixel value calculated from thesub-array 218. The average pixel value is 143. The result of subtractingthe error of −41 diffused from the previous average pixel value from theaverage pixel value 143 is 184. As the pixel value 518 has already beendetermined to be set to “on”, the tests are not carried out and an errorvalue of 255−184=71 is generated and subtracted from the average pixelvalue of the sub-array 220.

Processing moves to the average pixel value calculated from thesub-array 220. The average pixel value is 137 to the nearest wholenumber. The result of subtracting the error of 71 diffused from theprevious average pixel value from the average pixel value 137 is 66.Although this is less than 127, the pixel value 520 has already been isset to “on”, so as to form a pair with the pixel value 510. An errorvalue of 255−66=189 is therefore generated and subtracted from theaverage pixel value of the sub-array 222.

Processing moves to the average pixel value calculated from thesub-array 222. The average pixel value is 127 to the nearest wholenumber, The result of subtracting the error of 189 diffused from theprevious average pixel value from the average pixel value 127 is −62. Asthis is less than 127, the error diffusion algorithm determines that thepixel value 522 should remain “off”.

The results of the corresponding series of tests are all negative so thepixel value 522 remains “off”. The horizontally adjacent pixel value 524is chosen as the adjacent pixel that is to remain “off” so that thepixel values 522 and 524 form a pair. An error value of 0-(−62)=62 isgenerated and subtracted from the average pixel value of the sub-array224.

Processing moves to the average pixel value calculated from thesub-array 224. The average pixel value is 133 to the nearest wholenumber. The result of subtracting the error of 62 diffused from theprevious average pixel value from the pixel value 133 is 71. As thepixel value 524 has already been determined to remain “off”, the testsare not carried out and an error value of 0−71=−71 is generated andsubtracted from the average pixel value of the sub-array 226.

Processing moves to the average pixel value calculated from thesub-array 226. The average pixel value is 131 to the nearest wholenumber. The result of subtracting the error of −71 diffused from theprevious average pixel value from the pixel value 131 is 202. As this isgreater than 127, the error diffusion algorithm determines that thepixel value 526 should be set to “on”.

The series of tests set out above is carried out, the results all beingnegative. The pixel value 526 is therefore set to “on”. There is no needto set a horizontally or vertically adjacent pixel value to “on” becausethe pixel value 516 is vertically adjacent to the pixel value 526 and isset to “on”, so that the pixel values 516 and 526 form a pair.

As can be seen from this simple example, the specimen multiple-bit imagedata of FIG. 3 have an average value of 136 to the nearest whole number.This corresponds to approximately 53%, the maximum possible value of themultiple-bit data being 255. Accordingly, five of the nine pixel valuesof the second intermediate array that correspond to the nine averagepixel values of the first intermediate array calculated from the ninesub-arrays shown in FIG. 3 are “on”. It is to be noted that theoperation of the computer program of the invention is such that, asshown in FIG. 7, isolated pairs of diagonally adjacent “on” pixel valuesdo not occur, pairs of diagonally adjacent “on” pixel values such as 510and 518, and 518 and 526, either forming a triplet with a third “on”pixel value such as 520 or 516, or forming a quadruplet, each of thepair of diagonally adjacent “on” pixel values forming a pair with a(shared) horizontally or vertically adjacent “on” pixel value.

Referring to FIG. 10, this represents a portion 600 of an output mediumon which an isolated triplet 610 of horizontally and vertically adjacentpixels 612, 614 and 616, an isolated triplet 618 of horizontallyadjacent pixels 620, 622 and 624, an isolated triplet 626 of verticallyadjacent pixels 628, 630 and 632, and an isolated triplet 634 ofdiagonally adjacent pixels 636, 638 and 640 have been marked.

In images produced by the computer program of the invention the isolatedtriplet 610 of horizontally and vertically adjacent marked pixels couldoccur, because the marked pixels 612 and 614 form a pair of verticallyadjacent dots, the marked pixels 614 and 616 form a pair of horizontallyadjacent dots, and the marked pixel 614 of each pair of dots forms pairswith two horizontally or vertically adjacent dots 612 and 614.

Similarly, the isolated triplet 618 of horizontally adjacent markedpixels could occur, because the marked pixels 620 and 622 form a pair ofhorizontally adjacent dots, the marked pixels 622 and 624 form a pair ofhorizontally adjacent dots, and the marked pixel 622 of each pair ofdots forms pairs with two horizontally adjacent dots 620 and 624.

Similarly, the isolated triplet 626 of vertically adjacent marked pixelscould occur, because the marked pixels 628 and 630 form a pair ofvertically adjacent dots, the marked pixels 630 and 632 form a pair ofvertically adjacent dots, and the marked pixel 630 of each pair of dotsforms pairs with two vertically adjacent dots 628 and 632.

On the other hand, the isolated triplet 634 of diagonally adjacentmarked pixels could never occur, because none of the marked pixels 636,638 and 640 forms a pair of horizontally or vertically adjacent dots.

As can be seen from FIG. 10, marking of the triplet 610 causes eightregions of the surrounding pixels also to be marked, the regions beingdenoted by reference numerals 642, 644, 646, 648, 650, 652, 654 and 656.Marking of the triplet 618 also causes eight regions of the surroundingpixels also to be marked, the regions being denoted by referencenumerals 658, 660, 662, 664, 666, 668, 670 and 672. Marking of thetriplet 626 also causes eight regions of the surrounding pixels also tobe marked, the regions being denoted by reference numerals 674, 676,678, 680, 682, 684, 686 and 688.

Marking of the triplet 634, on the other hand, would cause twelveregions of the surrounding pixels also to be marked, the regions beingdenoted by reference numerals 690, 692, 694, 696, 698, 700, 702, 704,706, 708, 710 and 712.

Were isolated triplets of diagonally adjacent pixels such as 634 to bemarked, as can happen using known computer programs, they would appeardarker than isolated triplets of horizontally or vertically adjacentpixels such as 610, 618 and 626, which would give rise to the appearanceof patterning of the image. By preventing marking of isolated tripletsof diagonally adjacent pixels, or isolated longer lines of diagonallyadjacent pixels, the invention eliminates a significant cause of theappearance of patterning of the image.

If in operation 140 it had been determined that single dots were to beused in portions of the image of which the densities of dots are low,the operation of the program would differ from that described above asfollows.

Where it is determined from an average pixel value of the firstintermediate array that a corresponding pixel value of the secondintermediate array should be set to “on”, a horizontally or verticallyadjacent pixel value will only be set to “on” to form a pair with thatpixel value if the average pixel value is greater than 26, that isapproximately 10%. Similarly, where it is determined from an averagepixel value of the first intermediate array that a corresponding pixelvalue of the second intermediate array should be set to “off”, ahorizontally or vertically adjacent pixel value will only be set to offto form a pair with that pixel value if the average pixel value is lessthan 230, that is approximately 90%.

Once all of the average pixel values of the first intermediate arrayhave been processed, the (M/4)*(N/4) “on” and “off” pixel values thatconstitute the second intermediate array are converted into an array ofM*N “on” and “off” pixel values. In the present case, each “on” pixel ofthe second intermediate array is converted into a block of 4*4horizontally and vertically adjacent “on” pixel values, which, whenmarked on an output medium constitute a 4*4 pixel dot.

If in operation 150 it had been determined that reduced-sized pairs ofdots were to be used in portions of the image of which the densities ofdots are low, isolated pairs of horizontally and vertically adjacent“on” pixel values of the second intermediate array would be identifiedbefore conversion of the second intermediate array into an array of M*N“on” and “off” pixel values. For each such isolated pair of horizontallyor vertically adjacent “on” pixel values of the second array, it wouldbe determined whether the average pixel values of the first intermediatearray corresponding to the pair of “on” pixel values are both less than51, that is 20%. If both average pixel values are less than 15, insteadof converting such pairs of horizontally and vertically adjacent “on”pixel values into blocks of 8*4 and 4*8 horizontally and verticallyadjacent “on” pixel values, the pairs would be converted into blocks of6*4 and 4*6 horizontally and vertically adjacent “on” pixel values, suchas give rise to the pairs 322 and 328 of dots shown in FIG. 5.

If in operation 160 it had been determined that reduced-size dots wereto be used, instead of converting each “on” pixel value of the secondintermediate array into a block of 4*4 horizontally and verticallyadjacent “on” pixel values, each “on” pixel value of the secondintermediate array would be converted into a block of 3*3 horizontallyand vertically adjacent “on” pixel values, such as give rise to the dots418 and 420 shown in FIG. 6.

In an optional feature of the invention, once the 1-bit image data havebeen derived, minimum and maximum values of the multiple-bit image dataare identified. That is to say, for 8-bit image data, pixel values of 0and 255 of the multiple-bit image data are identified. For eachidentified pixel value of 0 of the multiple-bit image data, thecorresponding pixel value of the 1-bit image data is set to “off”. Foreach identified pixel value of 255, the corresponding pixel value of the1-bit image data is set to “on”.

The effect of this is that fine details of the image that is representedby the multiple-bit image data, such as text and straight lines ingraphics, are preserved in the image produced when the 1-bit image dataare printed.

FIGS. 8 a, 8 b and 8 c show typical patterns of dots produced in imagesby the invention for densities of dots of approximately 20%, 50% and80%, respectively. It can be seen that, in essence, the inventionprovides an FM screening process that produces images made up, inportions of the image of which the densities of dots are s low, of pairsof horizontally and vertically adjacent dots, in portions of the imageof which the densities of dots are higher, of chains of similar numbersof horizontally and vertically adjacent dots, in portions of the imageof which the densities of dots are higher still, of chains of similarnumbers of horizontally and vertically adjacent non-dots, and inportions of the image of which the densities of dots are highest, ofpairs of horizontally and vertically adjacent non-dots. Pairs ofisolated diagonally adjacent dots, that is diagonally adjacent dotssurrounded by non-dots, are avoided as far as possible.

FIG. 9 shows, for the purpose of comparison, a typical pattern of dotsproduced in images by known FM screening processes for densities of dotsof approximately 50%. The dots form a characteristic “chequer board andthin line” pattern which, when repeated across a portion of an image, isvery conspicuous. Where such a pattern of dots is printed using anoutput device that produces dot gain, the large numbers of isolateddiagonally adjacent dots produce a severe appearance of patterning ofthe image.

It will be appreciated that the foregoing description relates to onlyone embodiment of the invention and that the invention encompasses otherembodiments as defined by the claims. In particular it will be apparentto a person skilled in the art that the program could be modified foruse with output devices that can accept multiple-bit image data, such as2-bit image data, and can vary the manner in which they mark an outputmedium, for example by marking regions of varying size of the outputmedium, in dependence upon the multiple-bit image data. It will also beapparent that other error diffusion algorithms could be used toimplement the invention, such as a two-dimensional error diffusionalgorithm instead of the simple, one-dimensional error diffusionalgorithm described above, an example of such a two-dimensional errordiffusion algorithm being the Floyd-Steinberg algorithm.

1. A computer system executed process for generating 1-bit image datafrom multiple-bit image data, the process comprising the steps of:receiving, by the computer system, multiple-bit image data comprisingmultiple-bit pixel values; and deriving, by the computer system, fromthe multiple-bit pixel values 1-bit image data comprising “on” and “off”pixel values, each pixel value of the 1-bit image data corresponding toa pixel of an output medium, which pixel an output device would attemptto mark when printing the 1-bit image data if the pixel value were “on”,the 1-bit image data producing when printed an image constituted by aplurality of densities of dots, the dots being arranged such that, atleast for densities of dots greater than a first threshold density, atleast a majority of dots form a pair with at least one horizontally orvertically adjacent dot, and for densities of dots less than a secondthreshold density, the image is substantially free of blocks of 2*2horizontally and vertically adjacent dots, the second threshold densitybeing greater than the first threshold density.
 2. The process of claim1, wherein at least for densities of dots greater than the firstthreshold density and less than a third threshold density, at least amajority of dots form a pair with one horizontally or verticallyadjacent dot, the third threshold density being less than the secondthreshold density.
 3. The process of claim 1, wherein for all densitiesof dots, at least a majority of dots form a pair with at least onehorizontally or vertically adjacent dot.
 4. The process of claim 1,wherein for densities of dots less than the first threshold density, atleast some of the dots have no adjacent dots.
 5. The process of claim 2,wherein for densities of dots greater than a fourth threshold density,at least one dot of at least a majority of pairs of dots forms pairswith two horizontally or vertically adjacent dots, the fourth thresholddensity being greater than the third threshold density and less than thesecond threshold density.
 6. The process of claim 1, wherein fordensities of dots less than a fifth threshold density, at least amajority of dots form chains of horizontally or vertically adjacentdots, the chains having similar numbers of dots, and the fifth thresholddensity being less than the second threshold density.
 7. The process ofclaim 1, wherein the second threshold density, for densities of dotsless than which the image is substantially free of blocks of 2*2horizontally and vertically adjacent dots, is halfway between a minimumavailable density of dots and a maximum available density of dots. 8.The process of claim 1, wherein each dot of the image corresponds to asingle pixel value of the 1-bit image data.
 9. The process of claim 1,wherein each dot of the image corresponds to a plurality of pixel valuesof the 1-bit image data.
 10. The process of claim 9, wherein theplurality of pixel values correspond to a rectangular or substantiallyrectangular block of horizontally and vertically adjacent pixels of anoutput medium.
 11. The process of claim 10, wherein at least one of theplurality of pixel values is “off”.
 12. The process of claim 11, whereinfor densities of dots less than the first threshold density, for atleast a majority of pairs of horizontally adjacent dots, at least thepixel values corresponding to a first column of vertically adjacentpixels and a last column of vertically adjacent pixels of the pair ofblocks of horizontally and vertically adjacent pixels are “off”, and forat least a majority of pairs of vertically adjacent dots, at least thepixel values corresponding to a first row of horizontally adjacentpixels and a last row of horizontally adjacent pixels of the pair ofblocks of horizontally and vertically adjacent pixels are “off”.
 13. Theprocess of claim 11, wherein for at least a majority of dots, at leastsome of the pixel values corresponding to at least one of first and lastcolumns of vertically adjacent pixels and at least one of first and lastrows of horizontally adjacent pixels of the block of horizontally andvertically adjacent pixels are “off”.
 14. The process of claim 1,wherein the step of deriving, by the computer system, from themultiple-bit pixel values 1-bit image data comprising “on” and “off”pixel values further comprises identifying, by the computer system,multiple-bit pixel values of the multiple-bit image data equal to aminimum available multiple-bit pixel value or a maximum availablemultiple-bit pixel value, and for each minimum available multiple-bitpixel value generating, by the computer system, a corresponding “off”pixel value of the 1-bit image data, and for each maximum availablemultiple-bit pixel value generating, by the computer system, acorresponding “on” value of the 1-bit image data.
 15. An output devicehaving computer readable storage media including computer-executableinstructions that when executed direct the output device to perform theprocess of claim
 1. 16. A method of electronically generating 1-bitimage data from multiple-bit image data, the 1-bit image data comprising“on” and “off” pixel values, each pixel value of the 1-bit image datacorresponding to a pixel of an output medium, which pixel an outputdevice would attempt to mark when printing the 1-bit image data if thepixel value were “on”, the method comprising the steps of: storing, by acomputer system, multiple-bit image data comprising multiple-bit pixelvalues in electronic memory; and deriving, by the computer system, fromthe multiple-bit pixel values and storing in electronic memory 1-bitimage data that produce when printed an image constituted by a pluralityof densities of dots, the dots being arranged such that, at least fordensities of dots greater than a first threshold density, at least amajority of dots form pairs with at least one horizontally or verticallyadjacent dot, and for densities of dots less than a second thresholddensity, the image is substantially free of blocks of 2*2 horizontallyand vertically adjacent dots, the second threshold density being greaterthan the first threshold density.
 17. A method of electronicallygenerating 1-bit image data from multiple-bit image data, the 1-bitimage data comprising “on” and “off” pixel values, each pixel value ofthe 1-bit image data corresponding to a pixel of an output medium, whichpixel an output device would attempt to mark when printing the 1-bitimage data if the pixel value were “on”, the method comprising the stepsof: storing, by a computer system, multiple-bit image data comprisingmultiple-bit pixel values in electronic memory; and deriving, by thecomputer system, from the multiple-bit pixel values and storing inelectronic memory 1-bit image data that produce when printed an imageconstituted by a plurality of densities of dots, the dots being arrangedsuch that, at least for densities of dots greater than a first thresholddensity, at least a majority of dots form pairs with at least onehorizontally or vertically adjacent dot, for densities of dots less thana second threshold density, the image is substantially free of blocks of2*2 horizontally and vertically adjacent dots, at least for densities ofdots less than a third threshold density, at least a majority ofportions of the image that could be occupied by a dot, but are not sooccupied, henceforth referred to as “non-dots”, form pairs with at leastone horizontally or vertically adjacent non-dot, and for densities ofdots greater than a fourth density, the image is substantially free ofblocks of 2*2 horizontally and vertically adjacent non-dots, the secondthreshold density being greater than the first threshold density, thethird threshold density being greater than the fourth threshold density,and the fourth threshold density being approximately equal to the secondthreshold density.
 18. A method of electronically generating 1-bit imagedata from multiple-bit image data, the 1-bit image data comprising “on”and “off” pixel values, each pixel value of the 1-bit image datacorresponding to a pixel of an output medium, which pixel an outputdevice would attempt to mark when printing the 1-bit image data if thepixel value were “on”, the method comprising the steps of: storing, by acomputer system, multiple-bit image data comprising multiple-bit pixelvalues in electronic memory; and deriving, by the computer system, fromthe multiple-bit pixel values and storing in electronic memory 1-bitimage data that produce when printed an image constituted by a pluralityof densities of dots, the dots being arranged such that, for densitiesof dots greater than a first threshold density and less than a secondthreshold density, at least a majority of dots form a pair with onehorizontally or vertically adjacent dot, for densities of dots greaterthan the second threshold density and less than a third thresholddensity, at least a majority of pairs of horizontally and verticallyadjacent dots form a triplet with one horizontally or verticallyadjacent dot, and for densities of dots greater than the third thresholddensity and less than a fourth threshold density, at least a majority ofdots form triplets with two horizontally or vertically adjacent dots,the second threshold density being greater than the first thresholddensity, the third threshold density being greater than the secondthreshold density, and the fourth threshold density being greater thanthe third threshold density.
 19. The method of claim 18, wherein foreach density of dots between the third and fourth threshold densities,at least a majority of dots form parts of chains of horizontally andvertically adjacent dots, and at least a majority of the chains do notdiffer in a number of dots constituting the chains by more than one. 20.A method of electronically generating 1-bit image data from multiple-bitimage data, the 1-bit image data comprising “on” and “off” pixel values,each pixel value of the 1-bit image data corresponding to a pixel of anoutput medium, which pixel an output device would attempt to mark whenprinting the 1-bit image data if the pixel value were “on”, the methodcomprising the steps of: storing, by a computer system, multiple-bitimage data comprising multiple-bit pixel values in electronic memory;and deriving, by the computer system, from the multiple-bit pixel valuesand storing in electronic memory 1-bit image data that produce whenprinted an image constituted by a plurality of densities of dots, thedots being arranged such that, for densities of dots greater than afirst threshold density, at least a majority of dots form a pair with ahorizontally or vertically adjacent dot, for densities of dots greaterthan a second threshold density, some pairs of dots form a triplet witha horizontally or vertically adjacent dot, and for densities of dotsgreater than a third threshold density, at least a majority of pairs ofdots form a triplet with a horizontally or vertically adjacent dot, thesecond threshold density being greater than the first threshold densityand the third threshold density being greater than the second thresholddensity, and for each density of dots between the first and thirdthreshold densities, numbers of dots constituting substantially allisolated groups of horizontally and vertically adjacent dots differingby no more than one.
 21. Computer readable storage media includingcomputer-executable instructions that when executed direct a computer toperform the method of claim
 20. 22. (canceled)
 23. A computer programmedto perform the method of claim
 20. 24. Computer readable storage mediaincluding computer-executable instructions that when executed direct acomputer to perform the method of claim
 16. 25. A computer programmed toperform the method of claim
 16. 26. Computer readable storage mediaincluding computer-executable instructions that when executed direct acomputer to perform the method of claim
 17. 27. A computer programmed toperform the method of claim
 17. 28. Computer readable storage mediaincluding computer-executable instructions that when executed direct acomputer to perform the method of claim
 18. 29. A computer programmed toperform the method of claim 18.